Soliton-potential interactions for nonlinear Schrödinger equation in R³
Deng, Qingquan · Soffer, Avy · Yao, Xiaohua
Original · EN
In this work we mainly consider the dynamics and scattering of a narrow soliton of NLS equation with a potential in R³, where the asymptotic state of the system can be far from the initial state in parameter space. Specifically, if we let a narrow soliton state with initial velocity υ₀ to interact with an extra potential V(x), then the velocity υ₊ of outgoing solitary wave in infinite time will in general be very different from υ₀. In contrast to our present work, previous works proved that the soliton is asymptotically stable under the assumption that υ₊ stays close to υ₀ in a certain manner.
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